A point of the form $alpha_1x_1+alpha_2x_2+….+alpha_nx_n$ with $alpha_1, alpha_2,…,alpha_ngeq 0$ is called conic combination of $x_1, x_2,…,x_n.$

• If $x_i$ are in convex cone C, then every conic combination of $x_i$ is also in C.

• A set C is a convex cone if it contains all the conic combination of its elements.

Conic Hull

A conic hull is defined as a set of all conic combinations of a given set S and is denoted by coni(S).

Thus, $conileft ( S right )=left { displaystylesumlimits_{i=1}^k lambda_ix_i:x_i in S,lambda_iin mathbb{R}, lambda_igeq 0,i=1,2,…right }$

• The conic hull is a convex set.
• The origin always belong to the conic hull.